diff --git a/cechmate/filtrations/base.py b/cechmate/filtrations/base.py index c55f1b7..bb4150e 100644 --- a/cechmate/filtrations/base.py +++ b/cechmate/filtrations/base.py @@ -28,7 +28,7 @@ def __init__(self, maxdim=None, verbose=True): self.simplices_ = None self.diagrams_ = None - def diagrams(self, simplices=None, show_inf=False): + def diagrams(self, simplices=None, show_inf=False, verbose=True, simplicial=False): """Compute persistence diagrams for the simplices. Parameters @@ -46,6 +46,6 @@ def diagrams(self, simplices=None, show_inf=False): """ simplices = simplices or self.simplices_ - self.diagrams_ = phat_diagrams(simplices, show_inf) + self.diagrams_ = phat_diagrams(simplices, show_inf, verbose, simplicial) return self.diagrams_ diff --git a/cechmate/filtrations/custom.py b/cechmate/filtrations/custom.py index 9027c7b..799236a 100644 --- a/cechmate/filtrations/custom.py +++ b/cechmate/filtrations/custom.py @@ -23,3 +23,11 @@ def build(self, simplices): """ self.simplices_ = simplices + + def diagrams(self, simplices=None, show_inf=False, verbose=True, simplicial=True): + """ + Redefine the Custom version of diagrams so that simplicial defaults to True, rather + than false. + """ + + return super().diagrams(simplices,show_inf,verbose,simplicial) \ No newline at end of file diff --git a/cechmate/solver.py b/cechmate/solver.py index 019590e..7c5cb99 100644 --- a/cechmate/solver.py +++ b/cechmate/solver.py @@ -5,7 +5,7 @@ import phat -def phat_diagrams(simplices, show_inf=False, verbose=True): +def phat_diagrams(simplices, show_inf=False, verbose=True, simplicial=False): """ Compute the persistence diagram for :code:`simplices` using Phat. @@ -19,12 +19,21 @@ def phat_diagrams(simplices, show_inf=False, verbose=True): show_inf: Boolean Determines whether or not to return points that never die. + simplicial: Boolean + Asserts that the filtration is a simplicial complex at every "dist," + not some other kind of topological complex. Defaults to not checking + to ensure speed of existing filtrations. + Returns -------- dgms: list of diagrams the persistence diagram for Hk """ + ## Check that the filtration is a simplicial complex at every time step + if simplicial: + simplices = _assert_simplicial(simplices) + ## Convert simplices representation to sparse pivot column # -- sort by birth time, if tie, use order of simplex ordered_simplices = sorted(simplices, key=lambda x: (x[1], len(x[0]))) @@ -59,6 +68,36 @@ def phat_diagrams(simplices, show_inf=False, verbose=True): return dgms +def _assert_simplicial(simplices): + + # Initialize a set to keep track of simplices + existing_simplices = set() + + # Initialize a list which is the (sub)filtration + # where the filtration is properly a simplicial + # complex at each point + simplicial_filtration = list() + + # Sort the filtration by the time at which each simplex is + for s,t in sorted(simplices, key = lambda x: (x[1],x[0])): + + # Sort to ensure a uniform representation + sorted_simplex = tuple(sorted(s)) + + if sorted_simplex in existing_simplices: + continue + + else: + existing_simplices.add(sorted_simplex) + + # Don't sort in the final filtration because the + # user might care about the order in which the + # 0-faces are listed + + simplicial_filtration.append((s,t)) + + return simplicial_filtration + def _simplices_to_sparse_pivot_column(ordered_simplices, verbose=False): """ diff --git a/docs/notebooks/BasicUsage.ipynb b/docs/notebooks/BasicUsage.ipynb index b1d9af4..398cb25 100644 --- a/docs/notebooks/BasicUsage.ipynb +++ b/docs/notebooks/BasicUsage.ipynb @@ -56,9 +56,9 @@ "output_type": "stream", "text": [ "Constructing boundary matrix...\n", - "Finished constructing boundary matrix (Elapsed Time 1.58)\n", + "Finished constructing boundary matrix (Elapsed Time 2.62)\n", "Computing persistence pairs...\n", - "Finished computing persistence pairs (Elapsed Time 0.559)\n" + "Finished computing persistence pairs (Elapsed Time 1.39)\n" ] } ], @@ -76,7 +76,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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yMrYzI4fkMqt10A9qv8cbd3a/RsIFTo8oWZaGdHtzQYt8qY6JUtVLk2y/Frg2R80pXnZtgRd+CCs/gv26wxUvw4GH5btVBYlXjCZOnJhTMYLchX3XAD08y92B1TmqOyNymdU66Ae13+OlGiY+eW4tx/zyb9zy53lp+daCDIooBx+fkSEfPeSIEcCWGnj9p/ltT4ESLUa58BlFk6se0hRgjIi8CJwIbC4G/xHkNqt10L2xZMdLp2cRbQb04rc3F69Hlo7Im/nPSMquzYmXDQDeeuutvIoRBCRIPmzd04BhwHJgB3B1EPXmilxltQ7yQZ3seOn6q5JF5PnpzQUp8jYmykjKsVfCvBdg9xaQZjDoxny3qCA599xzWbhwIUce2SRLVc4IKsouma1bgZuCqKuUCbo3luh4gye8nVbPItmD3m9vLiiRj9cLVGDwhLdLxp9kZEDnI+CGGbDqY+hwCHQ9Jt8tKhjC4TDXXHMN1157LaeddlpexQgsU0PBEXRvLN7x0u1ZxBMAyM+MsbF6gREsnNxooH1P52M04PUZDRo0iNNOOy3fTbJcdoVELgeLphtYECvIA2D/fVrEDITI9jl5AzJiYTn2DKMpXjGqrq7mppsKw4BlPaQCwY9PJ8jw5nT9VamYFdOZuTad84v0AnuPnxpzLIH5kwxjL9FiFOR8RpliglQgJIsWC3rQbCb+Kr9mxVQi4II4v1yOGTOMYqVZs2a0adOm4MQITJAKhmQ+nWyEN2c7ejAVP1UQ5xd0lKJhlBLhcJgNGzbQuXNnnnvuuaxNIZEJ5kPySbZ9Icl8OsUY3pyKnyqo82vVYu8l3b51bL+WYZQbETPdKaecwo4dOwpSjMAEyRd+swH4Ea14ZZJlhCjGKR9SyXKR6flF/kcbd4Qb1u2uq0+htYZRmnh9RjfffDP77LNPvpsUFzPZ+SCeOen2l+Zz65/n0bV9a4b278Qrs2uTBiUk85PE8+kUozkqFT9VpudnGRsMoymFkA4oFUyQfBDPbBSZyK52006en7mySYRX9AMx2UMzkU8nlymMgiT6nCI9xOhzyPT8itGkaRjZ5u677y4aMQITJF8kGgwaIV5acu8DMdOHZq5SGGWLZD1Ev+cXKzy8FCPsROQp4HzgG1VtMoReHEdANU5arh3ASFWdk9tWGoXMuHHjOProo7n88svz3RRfmA/JB/EGg/rB+0AsRj9QqiTyoyXqIaZy/Fj+vKH9O+UsK3sOeYYSnYnZyB7hcJgHHniA3bt307Fjx6IRIzBB8kUkG0BFipEp0Q/EXE5lkQ+SBX8EYVaLJ2rvLFmb0hQaxYCqvgdsSFCkYSZmVZ0JtBeRg3LTOqMQifiMfvrTnzJ9+vR8NydlzGTnk4sGduPWP8/zXV6AS45rbIIqVj+QX5L5yIIwqyUStWI3aaZB0c7EbARPdADDhRdemO8mpYwJUgr48SVFUOCdJWubrC/lh2ayHlAQkYKl6CvKgKKdidkIlmKLpouHmexSYGj/Tk2eAIl8S+UW4ZXMR5bqzLSxKHWzZ4oU7UzMRrD861//4h//+EdRixFYD8k3k+fW8srs2kavnxGz3DtL1gY+M2sx4qcHlGkPsdTNnilStDMxG8FQX19Ps2bN6N+/P8uWLaNjx475blJGmCD5JJZ/JGKWG3d2P8a9PJ/wnr1y1aJCMpqZtRjJlViUstnTS6nPxGxkRigUYsSIERx//PHceeedRS9GENwU5ufgjIeoAJ5Q1QlR24cArwFfuKteVdV7g6g7VySNEIu2yrvL5ZZBoFzEIhfYTMxGPCJiNGnSJIYOHZrv5gRGxoIkIhXAw8BZODbtT0Rkiqoujir6vqqen2l9+TJ/JXKmPzB9KeH6xooUrteGdsai3PxLhmEEg1eMit1nFE0QQQ0nAMtVdYWqhoAXccZHBI7fJKex9ks3U3dk39pNO2MGNIw7u19C0SmHwbCGYeQGVeWyyy4rSTGCYAQp3liIaE4Skfki8rqIHJFORemM9E9XxKL3BccKFxElb4RYItGxqDDDMIJCRBg2bFhJihEEI0h+xkLMAQ5W1QHA74HJcQ8mMkpEZonIrLVrG4/jScf8lUm6mniBDBUiTTJxxxOdIEKdDcMob0KhELNnzwbgmmuuKUkxgmCCGpKOhVDVLZ7v00TkERHpqKrrog+WaABfOoMiM/HhJMryHZ0UFOJHl5mjPz7lEhJvGOkS8Rm98cYbLFu2jO7du+e7SVkjCEH6BDhURHoDtcAI4DJvARHpAqxRVRWRE3B6ZutTrSidkf6ZjOxPlJkhOlLO7zQLxl7KKSTeMNLBG8BQXV1d0mIEAZjsVLUOGANMBz4DXlLVRSIyWkRGu8W+D3wqIvOBicAIN2Q1JdIxf2Xiw0mW5TteDyoTv1U5EUT2b8MoVaLFaOzYsfluUtYJZBySqk7DGaTnXfeo5/tDwENB1JWq+SuTwZqRMre/NL9hMj4v8XpZ5Tb2KF0sJN4w4vPkk0+WlRhBmWRqyMSHE9kvFVOhPWj9YYlSDSM+119/PYcccghnnXVWvpuSMyy5qg9SNRXa2CN/5CMkPpMxaYaRbcLhMGPHjuXf//43zZo1KysxgjLpIQVBKr2sIKZZKAdynSjVgiiMQsY7hcQxxxzDNddck+8m5RwTpCxgGan9k8uQePPtGYWKV4yqq6vLUozABClr2NijwqMYfXs+Ehe3A/4I9MS5n3+rqk/nvKFG2kSLUbkEMMTCfEhG2VBsvj1P4uJzgcOBS0Xk8KhiNwGL3SwoQ4D/KyItc9pQIyN27NjBypUry16MwHpIWcGyDxQmRejba0hcDOBOxDcc8GbSV6CtiAiwL7ABqMt1Q43UCYVC1NfX065dOz788ENatrT3CBOkgDHHeeFShL69WImLT4wq8xDOzLGrgbZAlarW56Z5RrpEBr3u3LmTqVOnmhi5mCAFjDnOC5si8+35SVx8NjAPOB34NvCmiLzvzR8JTtJiYBRAz549s9BUwy/RGRiaNTPPSQT7JQKmGB3nRsGSNHExzrTlr6rDcpxZmftHH0hVH1fVSlWt7NSpU9YabCSmHNMBpYIJUsAUm+PcKGgaEhe7gQojcMxzXlYCZwCISGegH7Aip600fHPDDTeYGCXABClgbEI+Iyh8Ji7+FXCyiCwE/g7cEWtaF6MwGDt2LH/4wx9MjOJgPqSAKULHuVHA+EhcvBr4bq7bZfgnFAoxadIkqqqqGDBgAAMGDMh3kwoWE6QsUGSOc8MwsoTXZ3TwwQczaNCgfDepoDFBShMba2SkioicDPTCc9+p6nN5a5CRVaIDGEyMkmOClCKT59byy78sYuOOcMM6G2tkJENE/gcnLHseEBkXoIAJUgli0XTpYYKUAtGDXr3EG2tkPSnDpRI4PJ2Zko3i44MPPuC1114zMUqRkhKkuycv5E//XMUeVSpEuPTEHvz6oqMCO36sQa9eoscaWdYGw8OnQBfgq3w3xMg+p59+OosXL6ZfP4uuTYVAwr5F5BwRWSoiy0VkfIztIiIT3e0LROTYIOr1cvfkhfxx5sqGqcb3qPLHmSu5e/LCwOpINrg1eqxRoqwNRnkgIn8RkSlAR2CxiEwXkSmRT77bZwRHKBTi0ksvZdo0JyjSxCh1Mu4heTISn4UzsvwTEZmiqt4EkOcCh7qfE4E/0DQnV0b86Z+r4q739pIyMaHFm3IbYo81SiVrg5n2Spbf5rsBRvbx+owGDx6c7+YULUH0kBoyEqtqCIhkJPYyHHjOTW8yE2gvIgcFUHcDe+KY5r3rIya02k07Ufaa0PxOYx1r0CtA+9YtGqY0906R3UxipSJr2pPKtF1G4aKq76rqu8CwyHfvuny3z8gcrxhNnDiRMWPG5LtJRUsQghQrI3H0q72fMoCTBFJEZonIrLVr1/puREWch793faYmtIsGduO+i4+iW/vWCNCtfWserDqGeT//boMYeYUllkjG6kmZaa8sOCvGunNz3gojUMLhcCMxuvnmm/PdpKImiKAGPxmJ/ZRxVqo+DjwOUFlZ6Tsi6dITe/DHmStjro8QROLTRINe4wU9VIhQr9rIFOc10cU7SUvIWvyIyA3AjUAfEVng2dQW+DA/rTKCoqKigi5dupgYBUQQguQnI7GfMhkR8RMlirKL5wMKKvFpPAGpV+WLCec1LCcKH89Gu4qNdPxpBeyDewF4HbgP8Ab8bFXVDflpkpEp4XCYNWvW0L17dx5++GEkjoXGSI0gBKkhIzFQi5OR+LKoMlOAMe6MlycCm1U18PDXX190VMIw72zPGOpX8JKFjwfdrmIinVD5Qg6vV9XNwGbgUgARORBoBewrIvuqatNuvVHQhMNhqqqqmDVrFosWLaJt27b5blLJkLEPyWdG4mk4KfGXA/+NY8LIObF8QJFghCDwm+k7kSkuG+0qJtLxpxWDD05ELhCRz3HmK3oX+BKn52QUERExmjRpEuPGjTMxCphABsb6yEiswE1B1JUp2Ux86jfTd7yeVLf2rZkx/vSstK1YSMfPF29b7aadTJ5bWyjC/mtgEPCWqg4UkaG4vaZEiMg5QDVQATyhqhNilBkCPAi0ANap6mlBNtxw8IqR+YyyQ0llasgWqfgn/Ahetk2HxUw8sVZg8IS3UxJ4oGBMd0BYVdeLSDMRaaaq74jI/Yl28DPGT0TaA48A56jqStckaGSBe++918Qoy9gEfUnIxhihbJsOi5l4Y70g/m+faJ8CMt1tEpF9gfeB50WkGqhLso+fMX6X4UxhvhJAVb8JuN2ly1cLYPrP4P3/B+HkEa0/+clPePHFF02Msoj1kJKQyD8REZB0IrxszqTYeM2esXo9sZLYRr7f8ud5MY9ZIOHzw4GdwC3A5UA74N4k+8Qavxed4aQv0EJE/oETSl4da0oLERkFjALo2bNnGs0vMdb/C546B8LbneVV/4TL/tykWDgc5v777+e2226jXbt2VFVV5bih5YUJUhKS+TQyifAq4FDlvBIR697jp8Yco1W7aSe9x09t8ptViMQcjFwI4fOqul1EDgYOVdVnRWQfHL9QIvyM32sOHAecAbQGPhKRmaq6LKr+tMb3lSxfvLdXjAA+/xvU10OzvUYjr8/osMMO45JLLslDQ8sLEyQSC0OyUG4/Pah4dRZqqHKhkMg35DWfzvr3Bl6ZXes7M0Y+EJHrcHooB+DMi9QNeBRHSOLhd4zfOlXdDmwXkfeAAcAyjPh0PLTx8gHfjitG1dXVJkY5ouR9SN7ccoMnvN3E/5DMR5QslDvd7A/FEKqcbxL5hiLsDO/hT/9cFTdDRgH55m4CBgNbAFT1cyBZAELDGD8RaYkzxi86Q/hrwCki0tztdZ2IM/zCSESv78Cw38KBh0OvU2DECw2bosXI5jPKHSXdQ/LTC0nWw0kWyp1u9ocg0hgVE+n62QB+MWURm3aG45aLl1i3XrVQxAhgt6qGIiP6RaQ5cdJnRVDVOhGJjPGrAJ6KjPFztz+qqp+JyBvAAqAeJzT802yeSMlwwnXOJ4pVq1YxY8YME6M8UNKCFE9sfvmXRSnlkUsUgJAohDsTU2Apkal5cnddfcLthew78vCuiNwFtBaRs3AGh/8l2U7Jxvi5yw8ADwTY1rKkrq6OiooK+vTpw5IlS9h///3z3aSyo6RNdvF6Gxt3hBtMdPHw+zCLF8INZGQKLCUyMU8mS7PUosLJWVgEv+V4YC2wELgeR2TuzmuLyonQdvh6IezaHHNzOBzmhz/8IXfddReAiVGeKOkeUiKneCJSfZjF6kENnvB2RqbAUiIT82TSMgqVBx9A5cEHFPRvqar1IjIZmKyq/udVMTJnwxfwzPmwpQZa7w9XvArd9k5aHZ2BwcgfJS1IscxpfvhW88w7jn4ewuUyFikT82Syl4pwvfLA9KXMGH96Qf6W4jiNfo6T71HcVXuA36tqsnFIRhB88DtHjAB2boR3fgNXvAJYOqBCo6RNdrHMae1bt4hZ1jvgY9POcMbZGOI9bAvMr5ETMjFP+om0K/BAkFtwouuOV9UOqnoATiTcYBG5Nb9NKxO0PuayqnLFFVeYGBUQJd1Dgqa9kFhzEQlNw538jCXyHjPaXGT56vYSK1quVQt/70LJMjdAwYv8lcBZqrouskJVV41SHjUAABjhSURBVIjIFcDfgN/lrWXlwuD/4wx83bYGvrUfnOZMSyUiXHzxxXznO98xMSoQSrqHFItYvaZ4wQ21m3bGHLvkJd44JsDy1UXhjZbbuMN/L/Sigd2YMf50Hqw6phiCF6Jp4RWjCK4fKXZ33QiWjofCmE/g2r/D2LmEugzko48+AqCqqsrEqIAQjTOGoxCorKzUWbNmZb2ewRPeThr8sP8+Lfj5BUfEDF7wO5VEOacKSuV3SkQuf0MRma2qlRkeY46qHpvqtmySq/uqEAmFQowYMYK//vWvLF26lN69e+e7SWVHovuq5E12fvAT/BB5o4fGY2f8RpCVe6qgoAYCF2EgyAAR2RJjveDMHGvkiIgYRXxGJkaFR9EKUpBvyn78FBDbr5TJtOWp+KmKnVQj7UqlN6mqyRKoGjkgWozMTFeYFKUPKVtzFM0YfzrdUkz5k+m05QUeIRYYqUTaZeP/a5Q3zz//vIlREZCRIInIASLypoh87v6NObxZRL4UkYUiMk9EMjZeZzMxabIw4+g3er+T7ZV7GHgqkxJa4tnCYVd4D6s37WRPfeH6mv0wcuRI3n33XROjAidTk9144O+qOkFExrvLd8QpOzRWtFE6ZLO3kSihZ7w3+kR+jYjpqXbTzibh5UUQIRYofv0/5d6bLBQ+rd3MyKc/Zt22EP27tOWF6wZxQJuW+W6Wb0KhEGPHjuW2226jb9++nHrqqflukpGETE12w4Fn3e/PAhdleDxfZLu3cdHAbsz7+Xd5sOqYjMK2vaYncMQoMgDXwsDjU+69yULh11MXs25bCIAlX2/lsff+lecW+SfiM3rsscd49913890cwyeZ9pA6q+pXAKr6lYjEm99Fgb+JiAKPubNXxsTPVMu5GnQa640+FWd7LNOTknqoc7lhg4r3IiLnANU40088oaoT4pQ7HpgJVKnqy0HUvSvcOMPBrlBqKbjyhTeAobq6muuuazrFhFGYJBUkEXkL6BJj089SqGewqq52BetNEVmiqu/FKuhnquV8JSZNNXTbTE/pUU6JZxMhIhXAw8BZODPDfiIiU1R1cYxy9+PMmxQYI0/uxW0vzaNencwal594cJCHT59/Pu5kXujUD06/G1rs7TlHi5HNZ1RcJBUkVT0z3jYRWSMiB7m9o4OAb+IcY7X79xsRmQScAMQUJL/kYzxKqqHb5TTnUdAU4XijbHACsFxVVwCIyIs4ZvLFUeVuBl4Bjg+y8neWfkMklmFXuJ4Plq+jb5e2QVaROvP+BK+Pc74vfxN2b4ELf9+wORQKsW7dOhOjIiVTH9IU4Cr3+1U40yk3QkTaiEjbyHfgu0BRzmiZao+nnOY8MrJCN2CVZ7nGXdeAiHQDvgc0mrQvGhEZJSKzRGTW2rX+Zr9Y/s22xstrt8UpmUNqo4J0a2YDjhBt376dfffdl7ffftvEqEjJVJAmAGeJyOc4ZoUJACLSVUQis1x2Bj4QkfnAx8BUVX0jw3rzQqrO9lRCnQ0jBhJjXbQZ+0HgDlVN6OBR1cdVtVJVKzt16uSr8tP7N3YJD+0Xz0WcQ3qc2Hi554kNZrphw4ZRV1dH8+ZFO96/7MnoP6eq64EzYqxfDQxzv68ABmRST6GQjrO9FExPpZI1oQipAXp4lrsDq6PKVAIvOtMu0REYJiJ1qjo508pvO6svXdq14vM12zjl0I6ccVjnTA+ZOUf/0Jn9dflb0LEvoZNubeQzMjEqbuy/lwLl6Gwv9xx8eeYT4FAR6Q3UAiOAy7wFVLUhIZuIPAP8NQgxco9XOIEMXiqvhsqrLYChBDFBSpFS6PGkQhA5+KyHlR6qWiciY3Ci5yqAp1R1kYiMdrcn9BuVOmPHjjUxKjFMkEqIbDz4Mw1dtx5WZqjqNGBa1LqYQqSqI3PRpkLh1ltv5bjjjrNxRiWECVIKFPKbfioP/lTOI9PQ9XLPcm5kSH09vDEelr4OHb5N+LyJvPDXd7jyyivp168f/fpZxGopUZTZvvNBoWeg9puQNNXzGNq/U5NQr1RC121wsJERs56Ejx+DzSsJf/42VeecxMiRI3n//ffz3TIjC5ggxWDy3FoGT3ib3uOnNkxhXugZqP0++FM5j8lza3lldm2jOGMBLjnOvx/N8tIVN6s27OD9z9eyYXsoPw3Y+CUA4T1K1cs7mTRrNdXV1ZYotUQxQYoiXg8i3sR9hfKmH+8B3651i0bLqfRY4uXie2eJv4GVYIODi5m3l6xhyG//wY+e/JhT/+sdvli3PdgK1i6FPwyG+3rAlJsd81w0/c8jXN/MEaMldVTfdK4FMJQw5kOKIl4PokKEPdo0tV6hvOmPO7sf4/53PuGoeWu2h+qYPLe2oUeTik8oCHNbOYbKlwq3/nl+wzxI23bXccfLC3hp9EmZH3jTKvh6Abzzn7DGTdoy5znoVgnHXdW47MEn88kx9/PX+26ketyPGHv/s02PV6KEw2FqamrYtWtXvpuSFq1ataJ79+60aNEieWEXE6Qo4j1s96jSukVFwWagvmhgN375l0Vs3NF4DqfwHm0wx6U6L1NQufjKLVS+VNgcNR/Ykq83Z37Q2tnw7IUQipGGaOtX7t81sHYJ2rEvst9BnHzxKJYsPZM+ffpkXn8RUVNTQ9u2benVqxfuwOeiQVVZv349NTU19O7dO/kOLmayiyLewzaS9ifoNECx/FXpsilKjCJEmx39zstk5rbypukjMICH4sxHY4tRizZw2IWOYD10PKGnL6Bq8Lf530fvByg7MQLYtWsXHTp0KDoxAmdQdYcOHVLu3VkPKYpE6YGCftMPeoxOvB5NhUha8zKZua28aSawx9OVbvOtNB8XW9fAjAdhTwjqo16aug6ENgfCPgdA3S6YUU1oxyZGuD6jU/75MoyONwl16VOMYhQhnbabIEWRy4dw0GN04olpdB0R/PiC0hHhQh6vZfhnT5TLdO3WNHwZe8Lw7Pmwbpmz3Gp/6HAIrF8O7XrCPh3hc3cap0WTCPX4ToMYVZ/zLW4+76jMTsIoKkyQYpArn0fQY3TiiWnEdxRNNgIyLDND6VIfc7rMJGyu2StGALs2wg+eggOPgC/eh1d/3LCpLrSTEU981iBGY8/qA0PuyrzhRtFggpRHsjGBXzwxzdWU4JaZoXRpUZGGy3nfzrBPB9ix3llu3srpIekemDy6UdEKgUN796D64h8z9sqLYL+ujWaDNUofC2rII7kKGsjGvEzxgjEsM0Pp0rxZGv6MlvvAFa9A71OhxyCoeh7a94SNKxv8SaE9yhcb6xER7j8Nxt56O3T4tolRgfDYY49x4403Nlp3xBFHsGTJksDrsh5SQKTjN8mlvypIM2Qis5xN2x4sInIOUI2T7fsJVZ0Qtf1yIOL13wbcoKrzg6i7RTMIe8aqdmjTMr0DdR0IV/1l73JdCN68G3DEaMTLO/lw1R6WjNmX9ru3ZtBiIxssWLCAgQMHNizv2rWLlStXcuihhwZelwlSAGTiN0lVKIIKGMjkOInMculMYmjERkQqgIdxZmOuAT4RkSmquthT7AvgNFXdKCLnAo8DJzY9WupEu4wyjvgKbYc374GVM2HNpw1iNGlJHRPPaUX71hVw8pjM6ihjFtRs4vmZK2nbqjk3DT2E/dN9gYhi4cKFXHPNNY2W+/btS0VFRYK90sMEKQBy5Te5e/JCnp+5suFBkW7AQKaBB4nMchYqHignAMvdWZcRkReB4UCDIKnqh57yM3FmlQ2EuqhMPmlF2Xl56SpY/iZAlBi15ubfPAYHDYCDjs6sjjJl1YYdXPr4TLaHnHv64y83MGXMdwI59qJFi7j44osbXki2bdvG+eefH8ixo8lIkETkB8AvgMOAE1R1VpxyCc0OxU4u/CaT59Y2EqMI6QhfpgKazCxnmRkCoxuwyrNcQ+Lez4+B17PVmB3hGLnm/PKP+xvECOD+D0KOGJ27Dzff+xAc+6MAWli+zF21qUGMABbUbGbLrjD7tfKfticWq1atolOnTo38RWPGjKFPnz5s376dG2+8kZYtWzJkyBAuv/zyjOqCzHtInwIXA4/FK+DT7FDU5MJv8sD0pU3EKEKqwpeqgEab94b278Qrs2t9meVsTFJGxLKRxbwMRGQojiDFfC0WkVHAKICePXsG1T7/zHqy0eLtJ7fk8PNGc8mtD0BFZg9NA/p1bkvzZkKdG5vf44DWtE13ILOHBQsWcMQRRzRat3jxYoYPH86rr77K97//fS644AKqqqoCEaSMouxU9TNVTTb/QoPZQVVDQMTsUDLkIloukeikKnzxyis0SV8UK/v5K7NrueS4bkmj9gp9DqkioAbo4VnuDqyOLiQiRwNPAMNVdX2sA6nq46paqaqVnTp1Sqsx6QTZNbBPR8J7lHve2cWW3co+x1/BJT950MQoIPp1actDlw3khF4HcEb/A3n26hMCyfKwcOFCDj/88EbrFi1axNFHH01NTQ09ejiXZ1D+pFyEfccyO8R9RRaRUSIyS0RmrV3rf5qDfJKNsOpo4omIQMrCF0tAI0SLRjzz3h9nrgTgd1XHMGP86THPtdDnkCoCPgEOFZHeItISGAFM8RYQkZ7Aq8CPVHVZjGMERloDY13C5z1I1WvCr94L8fruSrhgYnANMwA458iDeGn0STw58nj6dNo3kGNGC9KGDRtQVTp37kz37t2pqakBoD7W1CFpkLRPJyJvAV1ibPqZqr7mow7fZgdw3uRwIoWorKzM4BbILdn2m8SKXhPg8kE9U67XG3gQy9To9Scl6pklC4awMUmZoap1IjIGmI7jf31KVReJyGh3+6PAPUAH4BH3jbhOVSvz1eYGNv4bdqyDzkcRVqHq1glMWriFidXVVNl8RkXD888/32j5gAMO4JtvvgHg4osvZsyYMUydOpULLrggkPqSCpKqnplhHb7MDkZigo5eiwho7/FTY74dREQjnn8sQqJgCBuTlDmqOg2YFrXuUc/3a4Frc92uhMx6CqbeDlpPuPNAqqa3Y9JrU5g4cSI333xzvltnBESbNm14+umnAz1mLkx2Sc0ORmIiWRFu/fM8ILGZLFWS+ZOG9u8U17wXIV6Px6avKFP+dg+oY8L5etlsPpn5gYmR4YuMBElEviciNcBJwFQRme6u7yoi08AxOwARs8NnwEuquiizZpcP2Q4MSOZP8gYwxCOeqOXCt2YUINKM8B5FVenRrhmLX55gYmT4IqO4QFWdBEyKsX41MMyz3MTsYPgj24Nu/fiT3lmylhnjT28yoBaS93hsTFL5ET7jV1SNvI6D2sBDo4fS9kQbY2T4w5KrFji5CAy4aGA3Zow/Pe58oJG6rMdjJCMcDlM14TUmfRam/0XjkJFToUWrfDfLKBIsdVCBk8vAAD91WY/HiEc4HKaqqopJkyaZz8hIC+shFTi5DAywIAQjE6688koTIyMjrIdU4OR6iopc1GXphEqTK664gsGDBzNmjGXsNtLDBKkIyKWZLNt12RTnpUU4HGbGjBkMGTKE8847L9/NMYocM9kZOcXSCZUOEZ/RGWecwbJlWc1aZJQJJkhGTrF0QsXLPi33Pi68AQy/+93v6Nu3bx5bZmSTXE5hboJk5JR40YGWTqjwEXdggFeMqqurGWu56UqaXE5hboJk5BSL5Ctedrmm1ldeecXEqBCZ/yI8+h14+jz4+tPADrtw4UKOPfbYRss2hblREtgU58VPVVUVvXr1YtCgQfluihHhq/kw+YaGHII8/wO4bTEEMCdS0UxhbhjpYINr/SMi5wDVONNPPKGqE6K2i7t9GLADGKmqc4Kou3WLioYAFN1TR/iD/2b+/O4MGDDAxKjQWL98rxgBbF0Nu7dCq/0yOmyiKcxXrFjBb37zGzZv3szLL7+cUT0RzGRnGAWKiFQADwPnAocDl4rI4VHFzgUOdT+jgD8EVf+d5/YHHDFaN+V+Vs2cysyZM4M6vBEkPQZBq3ZRy5mJEcSfwvyoo46iT58+PPnkk3H2TA/rIRlG4XICsFxVVwCIyIvAcGCxp8xw4DlVVWCmiLQXkYNU9atMK58yfzW6p461U+5n57KPGDbqLq6//vpMD2tkg3bd4JrpMOd/4Ftt4aSbAjlsoinMs4EJkmEULt2AVZ7lGuBEH2W6AY0ESURG4fSg6Nmzp6/K93jEaP8zr+eE8y9LrfVGbjnwMDjnPwM95MKFCxv5i7xTmGcDM9kZRuESyyMdPcGvnzKo6uOqWqmqlZ06dfJV+djT+9BsT4j9z7yew874Idee0sfXfkbp8Pzzz3PppZc2LHunMF+/fj2jR49m7ty53HfffYHUZz0kwyhcaoAenuXuwOo0yqREKBRi586dDD28OyvmvM9Xm3dzyIH70uZb9rgw9tKhQwceffTRQI9pV1iZYAlNi5JPgENFpDdQC4wAou1mU4Axrn/pRGBzJv6jUCjEiBEjWLVqFR9++CEH7teaA/ezQctGbjBBKgMsoWlxoqp1IjIGmI4T9v2Uqi4SkdHu9kdxZmIeBizHCfu+Ot36ImIUmUKiRYsWmZ+EYaRARoIkIj8AfgEcBpygqrPilPsS2ArsAepUtTKTeo3UyPY06Eb2UNVpOKLjXfeo57sCGYdURYuRzWdk5INMe0ifAhcDj/koO1RV12VYn5EGltDUSMbtt99uYlSAqGpDhoRiw3lXSo2MBElVPwOK9gcrF3I5DbpRnNx+++0ce+yxXH112hY/I2BatWrF+vXr6dChQ9E9Y1WV9evX06pVq5T2y5UPSYG/iYgCj6nq4/EKpjNewkjMuLP7NfIhgSU0NRwz3VNPPcWoUaPo1auXiVGB0b17d2pqali7dm2+m5IWrVq1onv37intk1SQROQtoEuMTT9T1dd81jNYVVeLyIHAmyKyRFXfi1XQFavHASorK1Pv8xlNsISmRjRen9EhhxzCmWeeme8mGVG0aNGC3r1757sZOSWpIKlqxleqqq52/34jIpNwUqLEFCQjO1hCUyOCqjaIUXV1tYmRUTBk3WQnIm2AZqq61f3+XeDebNdrGEZsVqxYwZw5c2w+I6PgyCh1kIh8T0RqgJOAqSIy3V3fVUQioaqdgQ9EZD7wMTBVVd/IpF7DMNJn8+bNJkZGQSLphOblChFZC/w7x9V2BEoxPN3OK3UOVlV/id+KiDTuq1K9dqB0z62QzyvufVXQgpQPRGRWKQ7ctfMy0qWUf+NSPbdiPS/L9m0YhmEUBCZIhmEYRkFggtSUuIN2ixw7LyNdSvk3LtVzK8rzMh+SYRiGURBYD8kwDMMoCEyQDMMwjILABCkGIvIDEVkkIvUiUnShk15E5BwRWSoiy0VkfL7bExQi8pSIfCMin+a7LaVCsmtFHCa62xeIyLH5aGeq+DivISKyWUTmuZ978tHOVEl2DxTj/8sEKTaReZ6KOt+eiFQADwPnAocDl4rI4fltVWA8A5yT70aUCj6vlXOBQ93PKOAPOW1kGqRwD7yvqse4n2JJbfYMie+Bovt/mSDFQFU/U9Wl+W5HAJwALFfVFaoaAl4Ehue5TYHgZovfkO92lBB+rpXhwHPqMBNoLyIH5bqhKVLO90DR/b9MkEqbbsAqz3KNu84wovFzrRTj9eS3zSeJyHwReV1EjshN07JO0f2/cjVBX8ER0DxPhU6saSYtzt+IhZ9rpRivJz9tnoOTX22biAwDJuOYuYqdovt/la0gBTHPUxFQA/TwLHcHVuepLUZh4+daKcbrKWmbVXWL5/s0EXlERDqqaqEmJ/VL0f2/zGRX2nwCHCoivUWkJTACmJLnNhmFiZ9rZQpwpRu9NQjYrKpf5bqhKZL0vESki4iI+/0EnOfi+py3NHiK7v9Vtj2kRIjI94DfA51w5nmap6pn57lZKaOqdSIyBpgOVABPqeqiPDcrEETkT8AQoKM7J9fPVfXJ/LaqeIl3rYjIaHf7o8A0YBiwHNgBXJ2v9vrF53l9H7hBROqAncAILYIUNrHuAaAFFO//y1IHGYZhGAWBmewMwzCMgsAEyTAMwygITJAMwzCMgsAEyTAMwygITJAMwzCMgsAEyTCMskdE9riZvueLyBwROdld31VEXo6zTy8RucyzPFJEHspVm0sREyTDMAzY6Wb6HgDcCdwHoKqrVfX70YVFpDnQC7gsepuRPjYw1jAMozH7ARvB6QUBf1XVI0VkJHAe0ApoA+wDHCYi84Bn3X26isgbwLeBSar605y3vogxQTIMw4DWrrC0Ag4CTo9T7iTgaFXdICJDgJ+o6vngmOyAY4CBwG5gqYj8XlVXxTmWEYWZ7AzDMPaa7PrjTHr3XCS/XRRvqmqiOYj+rqqbVXUXsBg4OBuNLVVMkAzDMDyo6kdAR5xcltFsT7L7bs/3PZgVKiVMkAzDMDyISH+cRKzJMn5vBdpmv0Xlg6m3YRjGXh8SOBPbXaWqe2Jb7RpYANSJyHzgGdxACCN9LNu3YRiGURCYyc4wDMMoCEyQDMMwjILABMkwDMMoCEyQDMMwjILABMkwDMMoCEyQDMMwjILABMkwDMMoCP4/7SWm2Z5t3voAAAAASUVORK5CYII=\n", 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" ] @@ -124,9 +124,9 @@ "output_type": "stream", "text": [ "Constructing boundary matrix...\n", - "Finished constructing boundary matrix (Elapsed Time 1.53)\n", + "Finished constructing boundary matrix (Elapsed Time 2.84)\n", "Computing persistence pairs...\n", - "Finished computing persistence pairs (Elapsed Time 0.924)\n" + "Finished computing persistence pairs (Elapsed Time 2.18)\n" ] } ], @@ -143,7 +143,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -181,13 +181,13 @@ "output_type": "stream", "text": [ "Doing spatial.Delaunay triangulation...\n", - "Finished spatial.Delaunay triangulation (Elapsed Time 0.000787)\n", + "Finished spatial.Delaunay triangulation (Elapsed Time 0.00475)\n", "Building alpha filtration...\n", - "Finished building alpha filtration (Elapsed Time 0.0354)\n", + "Finished building alpha filtration (Elapsed Time 0.0706)\n", "Constructing boundary matrix...\n", - "Finished constructing boundary matrix (Elapsed Time 0.00469)\n", + "Finished constructing boundary matrix (Elapsed Time 0.00674)\n", "Computing persistence pairs...\n", - "Finished computing persistence pairs (Elapsed Time 0.00063)\n" + "Finished computing persistence pairs (Elapsed Time 0.00155)\n" ] } ], @@ -204,7 +204,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -237,18 +237,18 @@ "output_type": "stream", "text": [ "Doing spatial.Delaunay triangulation...\n", - "Finished spatial.Delaunay triangulation (Elapsed Time 0.775)\n", + "Finished spatial.Delaunay triangulation (Elapsed Time 1.71)\n", "Building alpha filtration...\n", - "Finished building alpha filtration (Elapsed Time 78.5)\n", + "Finished building alpha filtration (Elapsed Time 151)\n", "Constructing boundary matrix...\n", - "Finished constructing boundary matrix (Elapsed Time 1.51)\n", + "Finished constructing boundary matrix (Elapsed Time 3.12)\n", "Computing persistence pairs...\n", - "Finished computing persistence pairs (Elapsed Time 0.161)\n" + "Finished computing persistence pairs (Elapsed Time 0.495)\n" ] }, { "data": { - "image/png": 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4cSKmTZsGALjxxhtRWVmJJ598EosWLYJUap3tvr6+8PX1tf8HICKXZ2v3icjISLHLIhckWs/Qx8cHycnJ2LVrl0X7rl27MGTIEJuvqaqqsgo8mUwGQRAg4jggInJB3IaJ2kLUpRbmzp2LiRMnYvDgwUhJScHq1auhVqsxffp0AMCkSZMQExNjHlk6evRoLFu2DAMHDsTNN9+Mc+fO4aWXXsKYMWMgk8nE/ChE5EIYhNRWoobh+PHjUVRUhCVLliA/Px/9+vVDZmYmunXrBqB2YmzDnuCLL74IiUSCF198EXl5eYiIiMDo0aOxdOlSsT4CEbmgM2fO4OLFiwxCajVR5xmKgfMMibzD7t270adPHwahB3LE73GuSEtEHkGj0UCn06FXr14AgOHDh4tcEbkT0adWEBF1VP09wmHDhuHcuXNil0NuiGFIRG6t4WAZTqWi9mIYEpHb4qhRsheGIRG5JQYh2RPDkIjczsWLFxmEZFcMQyJyO/7+/ggODmYQkt1wagURuZ2wsDDs3r0bVVVViI2NFbsc8gDsGRKRW9BoNFi7dq35cVhYGIOQ7IY9QyJyeQ0HywDAlClTxC2IPA57hkTk0hqPGr3rrrvELok8EMOQiFwWp0+QszAMicglMQjJmRiGRORytFotg5CcimFIRC4nKCgIkydPZhCS03A/QyJyWVqtlj+nZMURv8fZMyQil6BWqzFp0iRUVFSY2xiE5CycZ0hEolOr1UhNTTXPI1y3bp3IFZG3Yc+QiETVMAh79OiBpUuXil0SeSGGIRGJpnEQcrAMiYVhSESiYBCSK2EYEpHTCYKABx98kEFILoNhSEROJ5FIsHr1atx0000MQnIJHE1KRE5jMpkgldb+Dd6/f3989913kEgkIldFxJ4hETmJRqPBoEGDcPDgQXMbg5BcBcOQiByuftHt48ePY9asWTCZTGKXRGSBYUhEDtV494nPP//cfKmUyFXwO5KIHIbbMJG7YBgSkUMwCMmdMAyJyCFef/11BiG5DU6tICKHWLZsGQBg3rx5DEJyeQxDIrKboqIihIWFQSKRwMfHB++++67YJRG1Ci+TEpFdaDQa3HTTTZg9eza8bM9w8gAMQyLqsIaDZXbs2IHi4mKxSyJqE4YhEXWIrVGjnTt3FrssojZhGBJRu3H6BHkKhiERtQuDkDwJw5CI2uXo0aPIzc1lEJJH4NQKImqXcePGYdOmTRg8eDCDkNwew5CIWk2j0UAqlSImJgZAbSASeQJeJiWiVqm/Rzhs2DDk5eWJXQ6RXTEMiahFDQfLmEwm7kdIHoeXSYkIACCYTCjZsAHaLzIhGAwwarUwFhejMDAQk0+fwoVLlzhYhjwWw5CIAACFr7+O4n+vs2jL1+sx5Vg2NHo9EmJiGITksXiZlIhgLC9HyYb/WbTl6/WYolFDo9cjTqHAuhuTGITksRiGRISKQ4cg1NRYtMkktb8g4hQKrI2LR2RFhTjFETmB6GGYkZGBhIQEKJVKJCcn48CBA80eX1paipkzZyI6OhpKpRJ9+/ZFZmamk6ol8iwln27Cr0NuxaXZc6yei5Qr8O/4eKyNi0e0QgG/pBtFqJDIOdp1z/Dy5ct4/vnnsWfPHhQWFlpt12I0Glv1Phs3bsTs2bORkZGBW2+9Fe+//z7S0tLwyy+/ID4+3ur4mpoa3H333YiMjMSmTZsQGxsLjUaDwMDA9nwMIq8h1NSg7ItMXM1SQREfj5AHHkDpxo34fcXbFsdd0utxsroad9f9TEXKFQAAaadOiH7tNafXTeQsEqEdG4+lpaVBrVZj1qxZiI6OhkQisXj+vvvua9X73HzzzRg0aBBWrlxpbuvbty/Gjh2L9PR0q+NXrVqFN954A6dPn4ZCoWhr2QAArVaL4OBglJWVISgoqF3vQeROBJMJmieeROWhQ+Y2WZcuECorYSovN7dd0uvxmEaNPL0ey7vG4O7ISATcOgTKvokIf+pJSOQcb0euwRG/x9v13X3w4EEcOHAAAwYMaPeJa2pqoFKpMH/+fIv2ESNG4PDhwzZfs337dqSkpGDmzJnYtm0bIiIi8Mgjj2DevHmQyWQ2X6PT6aDT6cyPtVptu2smckeVBw9aBCEAGAsKLB7XB2H9YJl+SiV0CV3QlzvVk5do1z3DuLi4Du9kfeXKFRiNRkRFRVm0R0VFoaDRD2q9nJwcbNq0CUajEZmZmXjxxRfx1ltvYenSpU2eJz09HcHBweYvjoYjd2AoKUHZ9u3Q7toFU6OBLW1VfeaMzfardRdXGgdh/T1CyVMTOnReInfSrjBcsWIF5s+fj9zc3A4X0PgSqyAIVm31TCYTIiMjsXr1aiQnJ+Phhx/GokWLLC6zNrZgwQKUlZWZvzQaTYdrJnKk8m/24uywVFz6v3nIe/oZ/JoyBFUqVbvfT5mYaLNdamo6CA8OC0f/exiG5D1afZk0NDTUIqQqKyvRs2dP+Pv7W92/Ky4ubvH9wsPDIZPJrHqBhYWFVr3FetHR0VAoFBaXRPv27YuCggLU1NTAx8fH6jW+vr7w9fVtsR4iVyDU1ODSokVAg0v7QmUl1I9PRe9v90EWEmL9Gr0ekmbuoXcaMgQBqamo2LvXov1qjdFmEOYO7IJH3tlhvw9F5AZaHYYrVqyw64l9fHyQnJyMXbt2Wax8v2vXriYH4Nx66634+OOPYTKZIJXWdmp//fVXREdH2wxCIndT/etZmEpKrNoFnQ55zz2Prm/8A/KwsNpjT59GwWuv4epRFeSRkej81JMIm2Ddm5NIJIh99x2oP16Lir+9CWndHY5gqRTDAgKwr6LCHITSmwdhxDsrIVN0cujnJHI17RpNai8bN27ExIkTsWrVKqSkpGD16tX44IMPcPLkSXTr1g2TJk1CTEyMeWSpRqNBYmIipkyZgqeffhpnz57F448/jmeeeQaLFi1q1Tk5mpRcmb6wEOeG3tHk84qYGHTf9ClMFRW4MO5PMDWaCB+zYgWC7r3H6nXnVHuhmzDD6r6IIAgoM5kgRPpj8Ibt8LExpYnI1bjMaFKZTIb8/HxERkZatBcVFSEyMrLV8wzHjx+PoqIiLFmyBPn5+ejXrx8yMzPRrVs3AIBarTb3AIHagTtff/015syZg6SkJMTExODZZ5/FvHnz2vMxiFyOIjIS8tgYGC7a3iJJn5eHizNn4erx44CNn7PSzz6zCsPKo0dR82htEObr9fiwuAjzIiLhI5VCIpEgRCZDWXISg5C8Wrt6hlKpFAUFBVZheOnSJfTs2RNXr161W4H2xp4hubLKH36A+qnpQDt/hvxvvhnd/r3W/Dhnw0eoXvwPSGC51uifQ0LwUlQXAIBRCvQ4chD+wZ3t8AmIHE/0nuE///lPALX3ID788EMEBASYnzMajdi/fz+uv/56uxRG5G2K1qxB4Rtvdug9gtLSzP99dv8X0NsIwjiFAtPCaoPPoJAi/ssvGITk9doUhsuXLwdQe59h1apVFqM6fXx80L17d6xatcq+FRJ5AWNFBX5/L6P9byCRIGzSJISMfwgAULB/N/RPPm8zCOsHyxilQOLh7yDjcoZEbQvDCxcuAABSU1OxefNmhIaGOqQoIm9T89tvEKqq2v163z59ULJxI4rXrQMEAQLQbBAKAPrsP8ggJKrTrgE0exvNVyKi9hFMJpRt2w7tzq8AmcxqUIy8SxeYrl6Fqays2ffRnT5t8VgCwCQImJl30SoIDTKg9xdfQhHOS6NE9dq98u7Fixexfft2qNVq1DRaLmrZsmUdLozIEwkmE0o+3oDyr76CRKkEBMFq3VAzhQKGwkLAZGrXuaQSCV6MjMJrhZfxXkwsohUKVCol6LV/H5RBkS2/AZEXaVcY7tmzB2PGjEFCQgLOnDmDfv36ITc3F4IgYNCgQfaukchjXH5tKUo+/rjZY2Th4Qh58AGYKipQ8p//tvkcDZc0HOTvj03dukMqkcAEIGnnN/BhEBJZadfapAsWLMBzzz2Hn3/+GUqlEp999hk0Gg3uuOMOPPjgg/aukcgjGEpKUPLppy0fqNcj8tlnIQu2XnqtJfl6PR5W/4bT1dXmNqlEAgFA1LZP4FM3nYKILLUrDE+dOoXJkycDAORyOa5evYqAgAAsWbIEr7/+ul0LJPIUht9/B/T6Fo/zq7u6EjRqJNDEovW21A+W+am6Gq9cLjDvLCMA6L1vL8L7cKd6oqa0Kww7depk3iOwa9euOH/+vPm5K1eu2KcyIg/j26MH5JHNX6KUhYUh8rm5tccnJMC3lfN2G48aXdE1BpK6HmGPr76Eogt7hETNadc9w1tuuQWHDh1CYmIiRo0aheeeew4//fQTNm/ejFtuucXeNRJ5BIlcjujXXsXFZ2dDqFthRh4RgS5LFqMmJwfSwEAEpaWZpztUfPcddKdOtfi+zU2fiNjxGZTduzvwUxF5hnYtx5aTk4OKigokJSWhqqoKzz//PA4ePIhevXph+fLl5rVFXRGXYyOxGUtLUb5vH6RKPwQMuwNSpdLmcedH/RE1Da662NJcEHbbthWd+vRxwCcgEpcjfo+LumuFGBiG5A6qfvwRv02c1OJxC/MvYatWaxWE3Td9Av9+vEdInskRv8fbdc8QAEpLS/Hhhx9iwYIF5s18s7KykJdne7V9Imq91u5s/2JUF4wNCrIIQt/lrzEIidqoXfcMT5w4geHDhyM4OBi5ubl44oknEBYWhi1btuC3337DunXr7F0nkcerOHQIZdu342pWNvQaTZPHlRuNCKxbF9hfKsXforsCqB01qr7/Vtybdr8zyiXyKO3qGc6dOxdTpkzB2bNnoWxwvyMtLQ379++3W3FEnkgwGFB9+jT0hYXmtqKP1kIzdRq027Y3G4T5ej0e+C0X71753fI9ASjfTse9Sz90VNlEHq1dYfjjjz/iqaeesmqPiYlBQUFBh4si8lSVhw/j3F3DcWHsOJxLvROX5s2HsbwcVzJa3rGi4WCZz7ValNetYyoA0C16Ej3uGevg6ok8V7sukyqVSmi1Wqv2M2fOICIiosNFEXkiY0UlLj7zLEwVFXUNRpRt2wZZWBhM5eXNvtbWqNFAmax2d4q/zsXAh59w/Acg8mDt6hned999WLJkCfR1q2lIJBKo1WrMnz8f99/P+xVEtpze+b9rQdiAdvduSMOa3g6tuekT8jnT0ZdBSNRh7QrDN998E7///jsiIyNx9epV3HHHHejVqxcCAwOxdOlSe9dI5DTf5X+HCV9MwE3rb8LkLyfjWOGxDr+nSTBhwYEFSD9uezcXvUaD//Utha29KZoLQsm9Q3HdU892uD4iaudl0qCgIBw8eBB79+6FSqWCyWTCoEGDMHz4cHvXR+Q0OaU5+Muuv8AgGAAAWYVZmPb1NHw+9nNEB0S3+313/bYLO3J2QJogQZkfEHzV8nkJgAcPCbC1CukPVVU2g/Dc1KEY88L77a6JiCy1OQxNJhPWrl2LzZs3Izc3FxKJBAkJCejSpYvF1jFE7uazs5+Zg7CezqjDCtUKJEUm4WzJWfQN64sxvcbAT+4HAMgpy8H7x9/HryW/ok9YHzyV9BQSghMs3uNfP/0LCr2AP5wVcCEKGJBrfe6mfmruCw4GANzk728OwoKnRmPMnH908NMSUUNtWoFGEASMHj0amZmZ6N+/P66//noIgoBTp07hp59+wpgxY7B161ZH1tthXIGGmvLU10/hcP7hFo/rFtQNm0ZvgrZGiz9t/xPKdNd2oQ/yCcKTSU/i6OWjyC3LRbegbsj56SAWrtehc/NjZMzy9Xr4SaUIqZtLWE8AcHnpTKTeP6stH4vI4zji93ibeoZr167F/v37sWfPHqSmplo8980332Ds2LFYt24dJk1qeRkpIlcTGxgL5Ld83G/a3/DXw3/FBe0FiyAEAG2NFm8efdP8OFebixf2GFsdhJf0ejymUaOTVIp/xcWbA1EAoJkwBPcwCIkcok0DaDZs2ICFCxdaBSEA3HnnnZg/fz7Wr19vt+KInOnP1/+51cd+ceEL/FL0S6uOvUHduosv9UGo0etRaTLhqql2SI0A4OTdPXHPS2taXR8RtU2bwvDEiRO49957m3w+LS0Nx48f73BRRM721YWvsEy1DKHKpqc4tIfEJMDYitvoDYMyHzdyAAAgAElEQVSw8WCZouReePCdHXati4gstekyaXFxMaKiopp8PioqCiUlJR0uisiZ/vXzv7Bctdwh7z32iAmB1c0f01wQXrgpFqPWfe6Q2ojomjaFodFohFze9EtkMhkMBkOTzxO5Gr1Jj3/9/C+7v69EEPDY1ybck9X8JdLmgvDUTVG4f90uu9dGRNbaFIaCIGDKlCnw9fW1+bxOp7NLUUTOUllTaTUIxh5GqATc20IQAoBBEKAXBKsgPDLAF1PX7bN7XURkW5vCcPLkyS0ew5Gk5E5ClCHoGdIT50ub31G+rVJO21pPxlq8jw/WxsVDIZGYg/CX6wIw9X8/2rUeImpem8Lwo48+clQdRKIJV4bjPOwbhjVyCWrHgVrL1+txoaYGQzp1AlAbiKg7+mwPfzywnUFI5Gzt3umeyBMUVBbgh4If7PqeEaUCgqqaDsIpGjX+kncRhysrze0CgJ8HheO+zNbtcE9E9tWutUmJPEXR1SIITfTg2uPObCMe3yXAx2j9XONFtxMa9Ah/igfGf3zAbnUQUduwZ0he7bqw6xDuF26X97r3RyOmf9W6IGw4WKYgLhTjvz5llxqIqH0YhuSVqg21k/8UUgWW3rYUCqmi1a9NKBDwwAET7lGZEHfZhG6XBUgEAY982/ylUVtBeLwLcOeultdDJSLH4mVS8irf5X+H9O/TkVOWA4VUgT5hfbDgpgW4LvQ6nCw62eLr7ztiwoR91iNFy/wAX7318UUGQ5NBmN0ZmLCPPUIiV8AwJK9RUFmAmbtnosZUA6B2wv3PV37G5C8n44bON7T4+uBKAeP3254y0XiPwnohMhkG+dVu99QwCNWdgAmHGIREroJhSF7ji5wvzEHYkEEw4HTJ6RZfn1AgQN666YNmMokEr3WJRqnRiM5yOQQAxxKAR75kEBK5Et4zJK9hMDW9VKDO2PLqSZfCJGhNFubr9Xjr90IY67YKlUkk5iA8HMsgJHJFDEPyGvd0vwfSJr7l5ZKWL5IUhkrwzYDmt6CoHyyzprgYK678bm4XAOy/Dpi2m0FI5IoYhuQ1ugd3x9+H/h3+cn+L9hvDb8QjMcNa9R4f3CttclZi41Gjj4TUbgclAPi+FzB9O4OQyFXxniF5lbSENAzvNhzZl7NxQXsBcYFxSLmgQuXul7CuWywgab7nF3AV0MkAZaO5hM1NnzgbBDy2g0FI5MoYhuR1FFIFboq+CX3D+mLtidXYdvx9HI7r2mIQDjhvxDPbhTYF4dEwYNJhBiGRq2MYklf6VvMtntn7DEyCCehke0uyelKTgBc2GZFsYy1vgyDgyYsam0H4U2dgEqdPELkF3jMkr2MwGTBv/7zaIGyFW38RbAYhAMglErwQEYmedVsxmbdhCgDGMwiJ3AZ7huT6TEbg16+AvCwgsi/Qdwwg92n3250pOYNKQ2XLB9YZe9g6NAVBgKTusurQgAAM6dQJcokEAoDzSuCBowxCInfiEj3DjIwMJCQkQKlUIjk5GQcOtG71/v/973+QSCQYO3asgysk0RgNwMcPAf97BDjwJvDZVOCjNKCmqn3v98MH+HnTo4DQup0qbj5lRGyRZdslvR6TNWrk1lybwF8fhD/2AEYfYxASuRvRw3Djxo2YPXs2Fi1ahOzsbNx+++1IS0uDWq1u9nW//fYbnn/+edx+++1OqpREcXoHcG63ZVveUeDY+ja/lfG7Vdj+7ctI99W3OFim3sQ9AhoeeUmvx2MaNY5evYqXC/Ih1IWqAOBIDDA5k0FI5I5ED8Nly5Zh6tSpmDZtGvr27YsVK1YgLi4OK1eubPI1RqMREyZMwOLFi9GjRw8nVktOl3fUdvvFo0B1GfDdSmDHXODYBsBgvdRaQwt+XolFkeEwtjIIE/JNiCy/9rg+COsHy7we3RWSuh7hoXhg6h4GIZG7EjUMa2pqoFKpMGLECIv2ESNG4PDhpre1WbJkCSIiIjB16lRHl0hiC+9juz0kFlg9DPhqPnB0DbB1OrD+/tqAzPw/4M3rgLf7AweXAyYTfin6BV8qWr+w6E2njUhfe+34xkHYcLDM7kTgCe5HSOTWRB1Ac+XKFRiNRkRFRVm0R0VFoaCgwOZrDh06hDVr1uDYsWOtOodOp4NOd23dSa1W2/6CyflufAD4fhVw+edrbSHxtYNqinMsj72wH/jPnyx7k7v/Chj1OBvTRKjakJBnwNwt1/5SbC4It9wGLPqQQUjk7lxiNKmk0WWrhiP1GiovL8ejjz6KDz74AOHhrdudPD09HYsXL7ZLnSQChR/w2JeAai1wKQuITAQGPw58/qzt421cVv0u+0N8L32gVaebs9mIW87A4j7hPwoLbQbhZ6P88NJbWW3+SETkekQNw/DwcMhkMqteYGFhoVVvEQDOnz+P3NxcjB492txmMtVeypLL5Thz5gx69uxp8ZoFCxZg7ty55sdarRZxcXH2/BjUXiYTIG3FlXplEHDrM5ZtXW6sHVxjwx5/P3zdyR9KQYBOAnwR4AvkfN7iaUYcNSLljPUo07926QIUAPMiI81BeKILGIREHkTUMPTx8UFycjJ27dqFcePGmdt37dqF++67z+r466+/Hj/99JNF24svvojy8nK8/fbbNkPO19cXvr7NrzBCdmYyAqe/uNaT6zEMqNYCYT1qw+/kFmDPq0DxeSDqRiDtdaD7rS2/r64CUH0EXDgAXPzR+vnuQ/FejRqrfBvcG2zlFApFjQmP7bp27FWTCX51QR0ik2FFTEzt2wFYNxz4+7u8NErkSUS/TDp37lxMnDgRgwcPRkpKClavXg21Wo3p06cDACZNmoSYmBikp6dDqVSiX79+Fq8PCQkBAKt2EonRAHz8IHD+mwaNEgBC7b2+lFnAl/NqHwPA5Z+AtaOAaXuA2OSm39dQA/z7j8ClbNvPS2TQjnoda7+cADRcWaYVI0eHq4x47GsBsrrH9fcIJ4WGYUJoqPk4AcB/xwfg74ttBDERuTXRw3D8+PEoKirCkiVLkJ+fj379+iEzMxPdunUDAKjVakhbcymNxGfQAVtnNApCwBx8pWrgqwXXHjd8/qN7gP/7DfDtZPu9T+9oOggBQDAif81wVEd3blPJN58y4smvr9XTcLDMupJi/Ck4GH7S2m2b1o9U4G8MQiKPJBGEVl5H8hBarRbBwcEoKytDUFCQ2OV4lk8mAb9sa//rO0UCD38MxP2h9n5i8XmgUzjgFwqsHQ3k7m/25dUSCYbHdUWZTNbscQ39L93QqlGjn6ZK8MrKX9r/2YjIbhzxe1z0niF5iKLzHQtCAKgsBNYMBzpFAPqrQE0FIFUASeOB3IMtvlwpCHihuBQvh4fBVHd5VCoI5v9uyE8nID3D2Kog3J0MBiGRh2MYkn1oL9nvvSp/v/bfJj1w7L+tful9FZW4UafDHn9/aCUSrA2x/qsxuELAO+8Yoax73FwQfpkagOdW8tIokadjGJJ9dB0I+AYBOnEXNfhVocAnQQEokkrxvZ/S5gCav62+FoQAsLeiwmYQfvXnSDz3yrdOq52IxMMwJPvwDQBGvw1smQ4YdS0f7wBZvr54okskaqS2R5BKTQLeW25EWKMlTOtHjN4ZEGAOwsPjIjGXQUjkNThMk+yn35+AOSdrB72IYFVoUJNBCADLVxjRuaZ2osdlvR6VpmtTMCaEhl4bLDPGH9PSGYRE3oRhSPYVEAFE9LX/+0oVLR5yQdH0Ma/+y4AudR3WfL0ekzRqTL+osQhEAcC3ozrjlX+oOlotEbkZhiHZX6I9N1uWAL1GANKWr+h3r9HbbH/1QwOuu1zbI8zX6zGlbrBMocGACqMRQG0QbkkLwF/eannUKhF5Ht4zJPuLtGfPUADOfd2qI31tTJn92yoDepZYB2H9YJmoukujayaG461FB+xYN1H7GY1G6PW2/7jzBgqFArI2zBe2B4Yh2V/sHwDfYEBX5tTTXm20UtH4Xc0HYf09wkMjIvHWIt4jJPEJgoCCggKUlpaKXYroQkJC0KVLF5s7GDkCw5DsT+4D3PUykPmcU05XJJViSedQ/OjrY277wykD/nS05SD85pF4zHp5p1PqJGpJfRBGRkbC39/faUHgSgRBQFVVFQoLCwEA0dHRTjkvw5DsL/cgsHOh0073RJcInK3bmURiEvDCRiOSc6/tSVhuMqLcZLKeRzg+FnMZhOQijEajOQg7d27bGruexs/PD0Dtdn6RkZFOuWTKMCT7qtY6da7hTz4+5iCUGQW8vsaI+CLLY67zVWJtXBwCpbJr0yfGBuCVxbucUiNRa9TfI/T39xe5EtdQ/++g1+sZhuRmTEZg3X1AmcZppzzsVxuEib+ZMOczE4IbTJ+4bDBgQN1fmNf51q45IwBY+4gf/vEyl1gj1+SNl0Ztcfa/A8OQ7Ofc7toNfZ3kR18frAwOxrNbjbj11LWRpPX3CK8YDFgTF28ORAHAtqlR+McL+5xWIxG5B4Yh2U9JrlNOUwMgIyQYa0KCcOdxwWYQ1g+WiZLXfoubAHz5XG8seGK7U2okIvfCSfdkP91udfgp1DIZxsVEY01oMCCR4I8/XFtBpqlRowYJ8NXs6/E8g5DIYYYOHYqpU6datWdkZMDf3x/GugUuXBXDkOynSz9gyDMOeesqiQRzI8MxKq4r1D61y66N+MGAmLrBMk0F4beJwM75ffDc9C0OqYuIaqdDHDt2DMnJyVbPqVQq9O/f3+mT6NuKYUj2NeJVYPpBIOlhu77t8rAQ7Orkb96SKemsAVP31E6f+N1gsBmEl0KAThOH4fnJW+1aCxFZOnv2LMrLy5sMQ1vtroZhSPbX5UZAX2nXt9wW0Mn832FaAfM2X5tHGCyToZePr0UQ6qXAuWeSMXHcSrvWQeQOcn6vwN7ThSiurGn5YDtQqVSQyWRISkqyaNfpdDh58qRbhCEH0JBjKDq1fEwrHVL64Gpdj1AiCFi40QjFtVuF8JFIsDwmBmVGIyLkchgkwM8LbsFTj3xktxqI3IHBaMJznx7HtmOXAAA+cikWpF2Px25NcOh5s7KyYDQam5wjWR+GO3bswHPPPQeTyYR58+Zh2rRpDq2rLdgzJMdIngxI7PPt9VJEOCCRoNNVAfM/MSL+CnBJr8eqoisQ6hbn9pFIECGXo9wHUP/1TjwykUFI3ud/P2rMQQgANQYTluz4BecKKxx6XpVKhXHjxiE7O9via+HChVAqlUhMTITBYMDcuXPxzTffICsrC6+//jqKi4sdWldbMAwdqMZgwvrvf8OM9Sq8uuMX5F6x76VDl6Y+Agimlo9rQalUit/rbrzP2WrCwJzaIHxMo8Y/r1zB+8XXlpsxAbjw4u0YNf69Dp+XyB19c7rQqk0QgH1nrNvtKTs7G8OGDcOAAQMsvoqLi5GUlAS5XI4ffvgBN9xwA2JiYhAYGIiRI0di507XWQ6Rl0kd6C//VWFPg2/OjT9q8NlfhqBPl0ARq3KCqyXAt290+G1+8vHBwogwQCJBVLGApFzBHIT1g2XuCwoGAJT5AlV/m4jxo5y3JiqRqwn192lTuz3k5OSgtLQUgwYNsnouKyvLfIn00qVLiImJMT8XGxuLvLw8h9XVVuwZOojqtxKLIASACp0Bq749L1JFTlR0HjBc7dBbfBIYgEe6RkFXrsD/fWrEG2uMVkG4Ni4eXRQKHOkDFC+8FXcyCMnLTUzpBrnUchmz6GAl0m7s4rBzqlQqSKVSDBgwwKLdYDDgxIkT5jAUbOw36kpLzzEMHeT877av0TfV7lE69wKkina/vEgqwWudQ6EwAC9vMGLwOQHFV62DMLouCBOeewwjx39oxw9A5J4GxIXg34/fhJQendE1WIkx/bti45Mp8Pdx3EXArKws9O7dGwEBARbtJ0+eRHV1tbnHGBMTY9ETvHjxotO2Z2oNXiZ1kEHxITbbB8bZbvcoNRWAydDul8+IDIcgkWDwORM6lwM1JhOm2gjC492BxFnTkDLUOfsmErmDW3uF49Ze4U47X3p6OtLT063a+/fvb9EbvOmmm/Dzzz8jLy8PQUFByMzMxMsvv+y0OlvCnqGD9IoMxOONhjPHhvphRmovkSpyotyDqF0Wu+12K33xi7J2hwll3RQpH6kUs8Ij0F3hg7Vx8aiIU2DWdCkGzL4PKXczCIncgVwux1tvvYXU1FQMHDgQL7zwgkvt28ieoQO9PDoRI2/sgq9PXkb3zv4YOyjGoZcrRKPNB5RBgE/d3MKgmOaPt0EA8GJ4GLYHXrvUktVTAr0MUBiBUUFBuDswED4SCf7VT4I1I15H98Q/2ukDEJEzjBkzBmPGjBG7DJs88Dez68hWl+ClbSdxKl+LQF85LpfrMOfu68Quy34uHQO2zQQu/wzI/YDBjwMjXgOiBwCdewNFZ1v9Vl/5+1kEYU1RDY6vvYS/D4vG7EMyBFYDcqkE39wowSMPTmIQEpFdMQwdpKrGgMfX/oiSqtrdq8t1Bry95yy6higx/g/xIldnBwYd8PFDQMXlusdXge/eA858CZTmtnqOYZVEglfDw7Cj07WVK2qKanDh7xeg/12Pz5GP0892Q/fLwJVAAWvueg29E8c54AMRkTfjPUMH+eZ0oTkIG9qc5TrzajokZ9+1IGyoJKdNk+3fDAvBjoBO5gW4GwahIkKBrlO6Qi+X4GxXID3lGQYhETkEe4ZOZrIx18Yt2WGptasSCbY0ujTaMAgT5ifAp7MPIAj4T7+5GDD48Q6fk4jIFoahgwzuFmqzvWuIn5MrcZCEO2oHymjb19NVy2SY0DUKhiZ6hA2DcM+wVYjsfps9qycissDLpA7y/QXbC9BeKu3YyiwuQ+4DTNgExN7U5peuCg7CqLiuKJVf+1vs0r8v2QzCH259h0FIRA7HMHQQH5ntf1pFE+1uKSoRmLYL6H1Pqw4vl0jwVGQ43gsNNt8jrBfzWAwCkgIsgnBbtwnw653qiMqJiCzwMqmDpF4fCV+5FDqD5WCSEYlRIlXkQEWtW291RlQEjvkpzY9NehOkito/DhShCnSf2x0A4Gs0YufNr6LzDffbvVQiIls8qJviWs5errAKQgD4349qEaqxM5MJqCqu/V9dOVB8rsWX/OTjYxGENUU1OPfiOZQeLrU4TiII2HnvegYhETkVw9BBXtx6wmb76QI3X6j7xCfAin7APxKAf/YHzu0BAlpeEf/vYdfWZK0fLFNzuQaF2wph0psAQUCg0YhtAxehc9eBjvwERERWGIYOcvKSVuwS7C/nW2DzE9dGkJaqgc+mAoMmN/uyAz4+OKH0BWA9arT7/3WHVCHF5NIyHH70RyT0/7OjPwURkRWGoYMYO77Ju+vZ/KR1m8kAlGmafMkVmRQzukYBEkmT0ycCDQY8+/j319Y2JSK3M3ToUEydOtWqPSMjA/7+/jAajSJU1XoMQwfxkKn11+RlARUFtp/LPdTky1aEhDQbhFKTCV+P2QJFUFcHFU5EjiYIAo4dO2beyLchlUqF/v37QyaTiVBZ6zEMHcTj/mGripp+Tmh670KVX+3l0dLDpVZBqDCZsHPoOwiIuN7e1RKRE509exbl5eVNhqGtdlfDqRUOIpcCNZ50qTQ+BfAJqN24t7FmVqHpajDiokKBiD9GAABChoTU9ggFAd/flwlFWDdHVUzknU7tAL59HSjJBeJuBka8CkT2degpVSoVZDIZkpKSLNp1Oh1OnjyJZ5991qHntweP68C4Co8KQgDwDahdgq0N8stNmFhUBggCJBIJIkdHwqezD3xMJnx173oGIZG9/XYY+GQiUHAC0GmBc7uAtX8Eqh07oC8rKwtGoxH+/v6QSCTmL6VSCYPBYO4Zjhs3DqGhoXjggQccWk97MAyp9XSt/4HSlJlw20eVeGtdCVZdvIy7KqvQv1qHmcWlODTyE0R36e/AQom81NGPrHeNqboC/LLNoadVqVQYN24csrOzLb4WLlwIpVKJxMREAMAzzzyDdevWObSW9uJlUmq9yEQg90CLh2nKTBj270rklAgAjOhRUo0VhpraJ2dlAeE9HVsnkbfSlTfR7tieYXZ2NhYvXowBAwZYtL///vtISkqCvG4d4tTUVOzbt8+htbSXS/QMMzIykJCQAKVSieTkZBw40PQv3A8++AC33347QkNDERoaiuHDh+OHH35wYrVeyqBr1Q9UwyDsESrBvsmdEB0oBZRhwII8BiGRI10/yrpNIgX6jHTYKXNyclBaWopBgwZZPZeVleUWg2cAFwjDjRs3Yvbs2Vi0aBGys7Nx++23Iy0tDWq17WXL9u3bhz//+c/Yu3cvjhw5gvj4eIwYMQJ5eR6yaa6r2r0YOL6h2UNsBWFccN232PNnau87EpHjDJgADJ4KSOqmMfgGAWPeAcISHHZKlUoFqVRq1Ss0GAw4ceIEw7C1li1bhqlTp2LatGno27cvVqxYgbi4OKxcudLm8evXr8eMGTMwYMAAXH/99fjggw9gMpmwZ88eJ1fuZbL/2+zTTQah3A+Ypard8omIHEsqBf64DJhzEnh8JzD3FDDwUYeeMisrC71790ZAgOUfuydPnkR1dbXNHqMrEjUMa2pqoFKpMGLECIv2ESNG4PDhw616j6qqKuj1eoSFhdl8XqfTQavVWnxRGxj1wC/bAX1ls4fllZtQWNkoCAdMBF4sAMJ7OalYIgIABEUD8bc45WpMeno6Tp8+bdXev39/CIKAgQPdY61hUQfQXLlyBUajEVFRltsaRUVFoaCgidVOGpk/fz5iYmIwfPhwm8+np6dj8eLFHa7VK1VeAT4aCVw50+Kht8TKsWuiP2ICpbVB6B8OjH3XCUUSkbu45557kJWVhcrKSsTGxmLLli34wx/+IHZZAFxkNKmk0UavQt28tJb84x//wIYNG7Bv3z4olUqbxyxYsABz5841P9ZqtYiLi+tYwd7iwLJmg1BdZkLJVQH9u9Ten7gltu7bKSYZmLzDGRUSkRvZuXOn2CU0SdQwDA8Ph0wms+oFFhYWWvUWG3vzzTfxt7/9Dbt377Za9aAhX19f+Pr62qVer/PL1iafUpeZkPrvSpRWA99M8jcHIvqOAcb/x0kFEhHZh6j3DH18fJCcnIxdu3ZZtO/atQtDhgxp8nVvvPEGXn31VXz11VcYPHiwo8v0TiYTUPm7zafqgzCnRECIEgjzq+vFy32BMf90YpFERPYh+mXSuXPnYuLEiRg8eDBSUlKwevVqqNVqTJ8+HQAwadIkxMTEID09HUDtpdGXXnoJH3/8Mbp3727uVQYEBFiNZqJ2MpmAbTMBY4256bxCjnKpFEGF1bjb1qhRhR8w9zTgF9LMGxMRuSbRw3D8+PEoKirCkiVLkJ+fj379+iEzMxPdutWuW6lWqyGVXuvAZmRkoKamxmptu1deeQV//etfnVm657laCmStA059DlysXcigTCrB7MgIHPVToqaoBur1F1DdOAhTngaGvwLIFCJ/ACKi9hE9DAFgxowZmDFjhs3nGi/dk5ub6/iCvFFVMfDeTVaXRpeHhuKonxL6Er15P0JlhAK7J/jWBmG/B4B7XhOpaCIi+3CJMCSRafOBfw4EDFetntrbyQ8AIPOXQRFW2/OLn5+AMl0xEDEAeGCNU0slInIEhiEBGx+1GYQAEGAyoVgmg9RXiu5zu8NYZYQiVIHA2L8AdyxycqFERI4h+nJsJDJdBZB31OZTmjITwr64Nu1F6iuFIlSBPwT1Qs+7ltSOHiUi8gDsGXo7qRyQ+ViMHAUs1xp9FEDJqC4ol0qRKgnCnJFrRSmViMhRGIbeTqEEIq6v3Rm7TuNFt//W3Yi4i/lAcBzw9LfsERKRx+FlUm9X8Ttw+RfzwyZ3nwjvA/zlMIOQiGwaOnQopk6datWekZEBf39/GI1GEapqPYaht7vyKyAYADQThP0fBqYfBJRBIhdLRK5IEAQcO3bM5t6FKpUK/fv3h0wmE6Gy1uNlUm9mMgH6q4BMgarqGvMSa+YgDFEAz54AQmLFrpSIXNjZs2dRXl7eZBjedtttIlTVNuwZeqvC08C7ycD6+wGjHv4KCebc4oueFivLzGQQErmZ0upS/Ovnf2HxkcXYfn479Ca9w8+pUqkgk8msNk3Q6XQ4efKkW+x2z56ht9ryFFCcY9E08844PDayC/zD44Ckh4DE+0Qqjoja4/eq3zEhcwLyK/MBAJt+3YTMC5lYedfKVm2L115ZWVkwGo3w9/e3+XxycjI0Gg0mTpyIwsJCyOVyvPTSS3jwwQcdVlNbsWfojbSXgPxj0JSZcP8nVSiqMtW2VxTC/8kvgYfXMwiJ3NB/T/3XHIT1DuUdwuFLhx16XpVKhXHjxiE7O9via+HChVAqlUhMTIRcLseKFSvwyy+/YPfu3ZgzZw4qKysdWldbMAy9kU8naMqlGPbvSmw+ZcCTO6rN7ZD5iFsbEbXbmRLbm3H/WvKrQ8+bnZ2NYcOGYcCAARZfxcXFSEpKglwuR3R0NAYMGAAAiIyMRFhYGIqLix1aV1swDB1E4cL/sprftRi23mQeLLPiHmXtE8lTuPMEkRvrG9bXZvv1Ydc77Jw5OTkoLS3FoEGDrJ7Lysqyeb/w6NGjMJlMiIuLc1hdbeXCv7Ldm1zmuOvzHaHRaDBs2DDkXNaiR3Qo9s3shbhuCcCwhcDwxWKXR0QdMKHvBMQExFi0DYsdhluib3HYOVUqFaRSqbnXV89gMODEiRNWYVhUVIRJkyZh9erVDqupPTiAxkFkUgkAQewyLJiDMCcHPXr0wL59+1zqLzMi6phwv3B8MvoTbD+3HepyNQZFDcLw+OEOHzzTu3dvq83VT548ierqaoseo06nw7hx47BgwQIMGTLEYTW1B8PQQWr0JrFLsDJp0iQGIZGHC/IJwqOJjzrtfOnp6UhPT7dq79+/PwThWodAEARMmTIFd955JyZOnOi0+lqLl0kdxOB6WYgPP/wQw4YNYxASkdMdOnQIGzduxNatW80DbH766RIlMC4AABZLSURBVCexyzJjz9BBZFIJTCbxL5MaDAbI5bX/N/fs2RN79+4VuSIi8ka33XYbTCYX7CXUYc/QQSIDxZ+ioNFokJSUhC+++ELsUoiIXBrD0EF6RQaKev76wTKnTp3CCy+8AIPBIGo9RESujGHoIKfztaKdu/Go0Z07d5ovlRIRkTWGoYNcqaxp+SAH4PQJIqK2Yxh6EAYhEVH7MAw9SEZGBoOQiKgdeCPJg7z22msAgBkzZjAIiYjagGHoIIG+UpRWO35OzeXLlxEeHg6ZTAaZTGZzJQgiImoeL5M6iI/C8X9nqNVqDBkyBJMnT4bRaHT4+YiIPBV7hg5SVePYcFKr1UhNTUVOTu1u9VeuXEFUVJRDz0lE5KnYM3SQyEBfh713wyCsHyzDICQiMQ0dOhRTp061as/IyIC/v7/LX71iGDrI+D/YHsAi7+BOKraCkINliEhMgiDg2LFjNjfyValU6N+/P2QymQiVtR7D0EF0BtuLdMs6sOkvg5CIXNHZs2dRXl7eZBjaanc1DEMHOXL+is32miZCsjV+/fVXXLx4kUFIRM2quZiHyu++h1HrnGUhVSoVZDIZkpKSLNp1Oh1OnjzpFmHIATQO4u9r+5+2IxtODx8+HF988QX69OnDICQiK4LRiPyXX0bZ5i2AIEDi54eo+fMROv4hh543KysLRqMR/v7+Np9PTk5GeXk57rzzTuj1ehiNRjzzzDN44oknHFpXWzAMHWRKSnfsOVVo1d4zIqBN76PRaFBdXY3evXsDqA1EIiJbSjdvRtlnm82PhatXUbB4MTrdcjN8unVz2HlVKhXGjRuHl19+2aL9008/xbJly5CYmAiJRIJvv/0W/v7+qKqqQr9+/fCnP/0JnTt3dlhdbcHLpA5y+3URuDEmyKJNJpFg+fgBrX6P+rVGhw0bhrNnz9q7RCLyMBV7vrFuNJlQ7uBNvbOzszFs2DDzDvb1X8XFxUhKSoJcLodMJjP3HKurq2E0GiEI4m+AXo89Qwf6dPoQrDuSi4PnitA1WIkpt3bH9V2CWnwdYL3otlKpdGyxROT2ZMG2f7/IAlv3e6c9cnJyUFpaikGDBlk9l5WVZXG/sLS0FHfccQfOnj2LN954A+Hh4Q6rq63YM3QgpUKGJ4f2xLrHb8Lf709qdxBysAwRtUbI+IeBRlMYZBHhCLznHoedU6VSQSqVYsAAy6teBoMBJ06csAjDkJAQHD9+HBcuXMDHH3+My5cvO6yutmIYuhgGIRG1l/+ggYjLeA9+/ftDFhqKgOF3odu/10EW0Mlh58zKykLv3r0REGA5HuLkyZOorq622WOMiopCUlIS9u/f77C62koiuNJFWyfQarUIDg5GWVkZgoIcd+mgPS5evIg77riDQUjkhaqrq3HhwgUkJCR45G2Ry5cvw8/PD0FBQdBqtUhJScGGDRuspmPUa+7fwxG/x3nP0IX4+/sjODiYQUhEHufixYuYOnUqBEGAIAiYNWtWk0EoBoahCwkLC8Pu3btRVVWF2NhYscshIrKb5ORkHDt2TOwymsR7hiLTaDRYu3at+XFYWBiDkIjIydgzFFHDwTIAMGXKFHELIiLyUuwZiqTxqNG77rpL7JKIiLwWw1AEnD5BRORaGIZOxiAkInI9LhGGGRkZ5rkkycnJOHDgQLPHf/bZZ0hMTISvry8SExOxZcsWJ1XaMVqtlkFIROSCRA/DjRs3Yvbs2Vi0aBGys7Nx++23Iy0tDWq12ubxR44cwfjx4zFx4kQcP34cEydOxEMPPYTvv//eyZW3XVBQEB577DEGIRGRixF9BZqbb74ZgwYNwsqVK81tffv2xdixY5Genm51/Pjx46HVavHll1+a2+69916EhoZiw4YNLZ7PFVag0Wq1Lrf6DRGJy9NXoGkrZ69AI2rPsKamBiqVCiNGjLBoHzFiBA4fPmzzNf/f3r0HRVX3fwB/L3uBuHsDNkRNvCCaofBIKN76KZJm5jSiZSiNjllYqJVipoIFaprTTKKN5IxdFBw08zKMihXmNRNBSshLiOBPGMQrSCKX7/OHD/s8y0X3LHuD837N7Iwcvmf389nVfXvOfs9+T5482WT8uHHjWhxfXV2Ne/fu6d0sqbi4GDNmzEBlZaVuG4OQiMi2WPU6w/LyctTV1cHT01Nvu6enJ0pLS5vdp7S0VNL4VatWIT4+3jQFS9T4OsJvv/3WKnUQEdHjWf0zQwBQKBR6PwshmmwzdvySJUtw9+5d3a24uLj1BRug8azRhIQEizwuERFJZ9Uw7Ny5M5RKZZOjurKysiZHfw28vLwkjbe3t4erq6vezdx4+QQRyc2IESMwa9asJts3btwIR0dH1NXVWaEqw1k1DDUaDQIDA5GRkaG3PSMjA0OHDm12n5CQkCbjDx061OJ4S2MQEpHcCCGQk5Ojt5Bvg6ysLDz33HNQNlp02NZY/btJFy5ciMjISAQFBSEkJASbN29GUVER5s6dCwCYMWMGvL29dTNLY2JiMGLECKxZswaTJk3Cnj17cPjwYRw7dsyabQB49BdiypQpDEIikpVLly6hoqKixTAMDQ21QlXSWD0Mp06dips3b2LlypUoKSnBgAEDkJ6eju7duwMAioqKYGf33wPYoUOHIjU1FR9//DGWLVsGX19f7NixA8HBwdZqQUehUGDz5s2YM2cO0tLSGIREZHFX/7yJM+mFuHujCtpe7gh5xRfuno5mfcysrCwolcom6xNWV1fj/PnziImJMevjm4LVrzO0NHNcn1JfX68X2E+aAERE1JgprjMsLbiLH9adhaj/79u6o5sG0+Ofh8bBfMc+H374IdatW9fi78+dO6cLyqqqKvTr1w9Tpkx57D6yus6wPSgqKsKgQYP0vkKOQUhE1vDnkf/XC0IAqLr7EH+fvWHWx83KysLkyZORnZ2td/voo4/g4OAAf39/3diEhASbOJPXGMOwFYqKijB69Gjk5ubi3XffRX19vbVLIiIZq66qkbTdVLKzszFq1CgEBATo3W7duoWBAwdCpXp0VHrp0iX89ddfGD9+vFnrMQbD0EgNQdgwWWbfvn16p0qJiCytx8DOTTcqgB7PNrPdRAoKCnDnzh0MHjy4ye/Onj2rN6nmgw8+aPZrNm0B372N0DgIOWuUiGxBv2FPwy/EC/jPJzUqtR1GvtbXrBNosrKyYGdnh4CAAL3ttbW1yM3N1YXhnj170KdPH/Tp08dstbSG1WeTtjUMQiKyVXZ2CvzfTH/8a8IzuFv+Dzy6ucDeUW3Wxzx79ix69+4NZ2dnve3nz5/HgwcPdEeMp06dQmpqKtLS0lBZWYmamhq4urpi+fLlZq3PUJxNKtG8efOQlJTEICQik5LTqhVbt27Fn3/+aVOzSXlkKNH69esBAIsXL2YQEhG1EwxDA9y8eRMdO3aEQqGARqPBhg0brF0SEVGbFRUVZe0SmuAEmicoLi7GkCFD8N5770FmZ5SJiGSDYfgY//ul2+np6bh165a1SyIiIjNgGLagudUnOnXqZO2yiIjIDBiGzeAyTERE8sIwbIRBSETWxLkJj1j6eWAYNnLmzBkUFhYyCInIotTqRxfHV1VVWbkS29DwPDQ8L+bGSysamTx5Mnbu3ImgoCAGIRFZjFKphLu7O8rKygAAjo6OslwBRwiBqqoqlJWVwd3dHUql0iKPyzDEo1OjdnZ28Pb2BvAoEImILM3LywsAdIEoZ+7u7rrnwxJkH4YNnxHa2dkhMzNTF4hERJamUCig1Wrh4eGBmhrzLrtky9RqtcWOCBvIOgwbT5bheoREZAuUSqXFw0DuZDuB5tq1a5w1SkREAGR8ZDhhwgTOGiUiIgAyPjJkEBIRUQPZHRk2XMjZrVs37Nu3D25ubrh3756VqyIiIkM1vGeb8sJ82YVhRUUFgEcr1vfv39/K1RARkbFu3rwJNzc3k9yX7Fa6r6+vx/Xr1+Hi4mKxC1rv3bsHHx8fFBcXm2xVZlvT3nts7/0B7LG9kEOPd+/eRbdu3XD79m24u7ub5D5ld2RoZ2eHrl27WuWxXV1d2+1fzgbtvcf23h/AHtsLOfRoZ2e6aS+ynUBDRETUgGFIRESyp4yLi4uzdhFyoFQqMWrUKKhU7ffMdHvvsb33B7DH9oI9Sie7CTRERESN8TQpERHJHsOQiIhkj2FIRESyxzAkIiLZYxiayMaNG/HMM8/AwcEBgYGBOHr06GPH79q1C/7+/rC3t4e/vz92795toUqNJ6XH5ORkDB8+HB06dECHDh0wZswYnD592oLVSif1NWyQmpoKhUKBV155xcwVtp7UHu/cuYPo6GhotVo4ODigX79+SE9Pt1C1xpHa4xdffIG+ffviqaeego+PDxYsWIAHDx5YqFrpfv31V0ycOBFPP/00FAoFfvzxxyfuc+TIEQQGBsLBwQE9e/bEV199ZYFKjSO1vx9++AFjx45Fly5d4OrqipCQEBw8eFD6AwtqtdTUVKFWq0VycrLIy8sTMTExwsnJSVy9erXZ8SdOnBBKpVIkJiaK/Px8kZiYKFQqlTh16pSFKzec1B5ff/11kZSUJLKzs0V+fr548803hZubm7h27ZqFKzeM1P4aFBYWCm9vbzF8+HAxadIkC1VrHKk9VldXi6CgIDF+/Hhx7NgxUVhYKI4ePSpycnIsXLnhpPb4/fffC3t7e7Ft2zZx5coVcfDgQaHVasX8+fMtXLnh0tPTxdKlS8WuXbsEALF79+7Hji8oKBCOjo4iJiZG5OXlieTkZKFWq8XOnTstVLE0UvuLiYkRa9asEadPnxYXL14US5YsEWq1Wpw9e1bS4zIMTWDIkCFi7ty5etv8/PxEbGxss+MjIiJEeHi43rZx48aJadOmma3G1pLaY2O1tbXCxcVFfPPNN+Yor9WM6a+2tlYMGzZMfP3112LmzJk2H4ZSe9y0aZPo2bOnePjwoSXKMwmpPUZHR4sXXnhBb9vChQtFaGio2Wo0JUPCYtGiRcLPz09v21tvvSWef/55c5ZmEob01xx/f38RHx8vaR+eJm2lhw8fIisrC2FhYXrbw8LCcOLEiWb3OXnyZJPx48aNa3G8tRnTY2NVVVWoqalBx44dzVFiqxjb38qVK9GlSxfMmjXL3CW2mjE97t27FyEhIYiOjoanpycGDBiAxMRE1NXVWaJkyYzpMTQ0FFlZWbpT+AUFBUhPT8eECRPMXq+ltPR+c+bMGdTU1FipKvOpr69HRUWF5Pea9vv1BBZSXl6Ouro6eHp66m339PREaWlps/uUlpZKGm9txvTYWGxsLLy9vTFmzBhzlNgqxvR3/PhxbNmyBTk5OZYosdWM6bGgoAA///wzpk+fjvT0dFy6dAnR0dGora3F8uXLLVG2JMb0OG3aNNy4cQOhoaEQQqC2thZvv/02YmNjLVGyRbT0flNbW4vy8nJotVorVWYen3/+Oe7fv4+IiAhJ+zEMTaTxclBCiMcuESV1vC0wtubPPvsMKSkpyMzMhIODg7nKazVD+6uoqMAbb7yB5ORkdO7c2VLlmYSU17C+vh4eHh7YvHkzlEolAgMDcf36daxdu9Ymw7CBlB4zMzORkJCAjRs3Ijg4GJcvX0ZMTAy0Wi2WLVtmiXItornnpLntbV1KSgri4uKwZ88eeHh4SNqXYdhKnTt3hlKpbPI/z7Kysib/G2vg5eUlaby1GdNjg3Xr1iExMRGHDx/GwIEDzVmm0aT29/fff6OwsBATJ07UbauvrwcAqFQqXLhwAb6+vuYtWiJjXkOtVgu1Wg2lUqnb1q9fP5SWluLhw4fQaDRmrVkqY3pctmwZIiMjMXv2bADAs88+i/v372POnDlYunSpSZcIspaW3m9UKhU6depkpapMb8eOHZg1axbS0tKMOgPV9l9pK9NoNAgMDERGRobe9oyMDAwdOrTZfUJCQpqMP3ToUIvjrc2YHgFg7dq1+OSTT3DgwAEEBQWZu0yjSe3Pz88Pf/zxB3JycnS3l19+GaNHj0ZOTg58fHwsVbrBjHkNhw0bhsuXL+uCHgAuXrwIrVZrc0EIGNdjVVVVk8BTKpUQjyYXmq1WS2rp/SYoKAhqtdpKVZlWSkoKoqKisH37duM/75U8TYeaaJjOvWXLFpGXlyfmz58vnJycRGFhoRBCiMjISL3ZbMePHxdKpVKsXr1a5Ofni9WrV7eZSysM7XHNmjVCo9GInTt3ipKSEt2toqLCWi08ltT+GmsLs0ml9lhUVCScnZ3FvHnzxIULF8T+/fuFh4eH+PTTT63VwhNJ7XHFihXCxcVFpKSkiIKCAnHo0CHh6+srIiIirNXCE1VUVIjs7GyRnZ0tAIj169eL7Oxs3eUjsbGxIjIyUje+4dKKBQsWiLy8PLFlyxabvrRCan/bt28XKpVKJCUl6b3X3LlzR9LjMgxNJCkpSXTv3l1oNBoxePBgceTIEd3vRo4cKWbOnKk3Pi0tTfTt21eo1Wrh5+cndu3aZeGKpZPSY/fu3QWAJrcVK1ZYvnADSX0N/1dbCEMhpPd44sQJERwcLOzt7UXPnj1FQkKCqK2ttXDV0kjpsaamRsTFxQlfX1/h4OAgfHx8xDvvvCNu375thcoN88svvzT7b6uhr5kzZ4qRI0fq7ZOZmSkGDRokNBqN6NGjh9i0aZPlCzeQ1P5Gjhz52PGG4hJOREQke/zMkIiIZI9hSEREsscwJCIi2WMYEhGR7DEMiYhI9hiGREQkewxDIiKSPYYhURtVWFgIhUJh9MoZhq6STiQHDEMiGxUVFQWFQqG7derUCeHh4cjNzQUA+Pj4oKSkBAMGDHjs/cTFxSEgIMASJRO1WQxDIhsWHh6OkpISlJSU4KeffoJKpcJLL70E4NEXSnt5eUGlan7xGfGf9fmI6MkYhkQ2zN7eHl5eXvDy8kJAQAAWL16M4uJi3Lhxo8lp0szMTCgUChw8eBBBQUGwt7fHd999h/j4eJw7d053hLl161bd/ZeXl2Py5MlwdHRE7969sXfvXit1SmRdDEOiNqKyshLbtm1Dr169HrsO3aJFi7Bq1Srk5+cjLCwM77//Pvr37687wpw6dapubHx8PCIiIpCbm4vx48dj+vTpuHXrliXaIbIpXNyXyIbt378fzs7OAID79+9Dq9Vi//79j110duXKlRg7dqzuZ2dnZ6hUKnh5eTUZGxUVhddeew0AkJiYiC+//BKnT59GeHi4iTshsm08MiSyYQ0LBufk5OC3335DWFgYXnzxRVy9erXFfaQspDxw4EDdn52cnODi4oKysrJW1UzUFvHIkMiGOTk5oVevXrqfAwMD4ebmhuTkZMyePbvFfQzVeKVzhUKht7I9kVzwyJCoDVEoFLCzs8M///xj8D4ajQZ1dXVmrIqo7eORIZENq66uRmlpKQDg9u3b2LBhAyorKzFx4kSD76NHjx64cuUKcnJy0LVrV7i4uMDe3t5cJRO1STwyJLJhBw4cgFarhVarRXBwMH7//XekpaVh1KhRBt/Hq6++ivDwcIwePRpdunRBSkqK+QomaqMUQghh7SKIiIisiUeGREQkewxDIiKSPYYhERHJHsOQiIhkj2FIRESyxzAkIiLZYxgSEZHsMQyJiEj2GIZERCR7DEMiIpI9hiEREckew5CIiGTv3zZzDVfe4CD1AAAAAElFTkSuQmCC\n", + "image/png": 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\n", 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" ] @@ -280,7 +280,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Custom filtration\n", + "## Custom filtration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using a filtration list\n", "\n", "If you have a point cloud and a set of simplices with times at which they are added, you can compute the persistence diagrams associated to the custom filtration you've defined. For instance, assume we want to compute a filtration where 4 vertices enter at time 0 and the edges and triangles are added in the pattern below (note how the triangles are not added the moment all of their edges are added, unlike Rips):\n", "\n", @@ -299,9 +306,9 @@ "output_type": "stream", "text": [ "Constructing boundary matrix...\n", - "Finished constructing boundary matrix (Elapsed Time 8.75e-05)\n", + "Finished constructing boundary matrix (Elapsed Time 0.000251)\n", "Computing persistence pairs...\n", - "Finished computing persistence pairs (Elapsed Time 5.08e-05)\n", + "Finished computing persistence pairs (Elapsed Time 0.000151)\n", "H0:\n", " [[ 0. 1.]\n", " [ 0. 1.]\n", @@ -331,12 +338,284 @@ "print(\"H1:\\n\", dgms[1])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Object oriented approach\n", + "\n", + "If you have an algorithm which defines your filtration, you can also define a custom filtration using the class `cechmate.filtrations.custom.Custom`. Just define a subclass of `Custom` which includes a `.build()` method, and use it like the `Alpha` and `Rips` examples above." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "%aimport cechmate.filtrations.custom\n", + "%autoreload 1" + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "from cechmate.filtrations.custom import Custom\n", + "\n", + "from math import factorial\n", + "\n", + "from itertools import combinations\n", + "\n", + "class SimplexSizeFiltration(Custom):\n", + " \"\"\"\n", + " This filtration takes in a list of points, and builts up a simplex\n", + " from them. The simplex has i-faces added at time i.\n", + " \"\"\"\n", + " \n", + " def build(self,X):\n", + " \n", + " simplices = list()\n", + " \n", + " n = len(X)\n", + " \n", + " for k in range(1,n+1):\n", + " \n", + " n_choose_k = int(factorial(n)/(factorial(k)*factorial(n-k)))\n", + " \n", + " simplices += list(zip(combinations(X,k),\n", + " [k-1]*n_choose_k))\n", + " \n", + " return simplices\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(('a',), 0),\n", + " (('b',), 0),\n", + " (('c',), 0),\n", + " (('d',), 0),\n", + " (('a', 'b'), 1),\n", + " (('a', 'c'), 1),\n", + " (('a', 'd'), 1),\n", + " (('b', 'c'), 1),\n", + " (('b', 'd'), 1),\n", + " (('c', 'd'), 1),\n", + " (('a', 'b', 'c'), 2),\n", + " (('a', 'b', 'd'), 2),\n", + " (('a', 'c', 'd'), 2),\n", + " (('b', 'c', 'd'), 2),\n", + " (('a', 'b', 'c', 'd'), 3)]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ssf = SimplexSizeFiltration()\n", + "simplices = ssf.build('abcd')\n", + "simplices" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Constructing boundary matrix...\n", + "Finished constructing boundary matrix (Elapsed Time 0.000219)\n", + "Computing persistence pairs...\n", + "Finished computing persistence pairs (Elapsed Time 0.00018)\n" + ] + }, + { + "data": { + "text/plain": [ + "[array([[ 0., 1.],\n", + " [ 0., 1.],\n", + " [ 0., 1.],\n", + " [ 0., inf]]),\n", + " array([[1, 2],\n", + " [1, 2],\n", + " [1, 2]]),\n", + " array([[2, 3]])]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplex_size_dgms = ssf.diagrams(simplices,show_inf=True)\n", + "\n", + "simplex_size_dgms" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_diagrams(simplex_size_dgms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is also possible to define something a little more general than a simplicial complex. For example, we can construct the two-sphere $S^2$ as the $\\Delta$-complex where there are 3 0-cells, with a 1-cell connecting each of them, and then two 2-cells with each boundary being the 1-skeleton consisting of 3 1-cells.\n", + "\n", + "To see how this could be used with persistence, add the i-cells at time/distance i." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "filtration = [('a',0),('b',0),('c',0),\n", + " ('ab',1),('ac',1),('bc',1),\n", + " ('abc',2),('abc',2)]" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Constructing boundary matrix...\n", + "Finished constructing boundary matrix (Elapsed Time 0.000179)\n", + "Computing persistence pairs...\n", + "Finished computing persistence pairs (Elapsed Time 0.000127)\n" + ] + } + ], + "source": [ + "S2_cell_dgms = cm.phat_diagrams(filtration,show_inf=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_diagrams(S2_cell_dgms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the infinite persistence comes from the true homology of $S^2$, which is\n", + "$$H_n(S^2) = \\begin{cases} \\mathbb{Z} & n=0,2 \\\\ 0 &\\text{else} \\end{cases}$$\n", + "\n", + "We could turn this into a simplicial complex by saying the two 2-cells `'abc'` and `'abc'` should only count once (which may be the intent of the given filtration in many circumstances). This is done by asserting that `simplicial=True` in the function call of `cm.phat_diagrams()`." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Constructing boundary matrix...\n", + "Finished constructing boundary matrix (Elapsed Time 0.000104)\n", + "Computing persistence pairs...\n", + "Finished computing persistence pairs (Elapsed Time 0.000132)\n" + ] + } + ], + "source": [ + "B2_simplicial_dgms = cm.phat_diagrams(filtration, show_inf=True, simplicial=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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